Summary: Pseudomodular lattices have been used by the first author and \textit{L. Lovasz} [Combinatorica 7, 39-48 (1987; Zbl 0627.05016)] in order to investigate combinatorial properties of algebraic matroids and were further analyzed by \textit{A. Björner} and \textit{L. Lovasz} [Acta Sci. Math. 51, No. 3/4, 295-308 (1987; Zbl 0643.05023)]. The purpose of our paper is to present local conditions, characterizing modular sublattices of a pseudomodular lattice. As an application, we derive a result by the second and the third author [Combinatorica 9, No. 2, 145-152 (1989; Zbl 0786.05017)], implying that Lovasz's min-max formula for matchings in projective geometries remains valid for pseudomodular lattices, and we discuss a relation with B. Lindströms construction of subgeometries of full algebraic combinatorial geometries which are isomorphic to projective geometries over skew fields.